Ionic bonds and Coulombs law

I bonds are the bonds that hold together ionic compounds. So basically, it's what holds together cations and anions. An example of a compound that's held together with ionic bonds is sodium chloride, also known as table salt.

So here, we have a close-up picture of some really nice crystals of sodium chloride. This is something that you could try at home. You can take some regular table salt that you might have, dissolve it up in some water, and then let that water slowly evaporate. If you're lucky, you might get some beautiful, symmetric crystals like these.

For me personally, at least, growing crystals that look beautiful is one of the most fun things about chemistry. You can see when we look at the close-up shapes of these crystals that they have some very beautiful symmetry. That symmetry tells us a little bit about the structure of these compounds on a molecular level.

If we zoom in on these crystals, we can imagine. Um, actually, we don't have to imagine. You can look at these with different kinds of instruments like X-ray crystallography, and you can look at the crystal lattice and get information about how the different ions are arranged in these solids.

So the way that the ions are arranged determines a lot of things about the properties of these compounds. These ionic bonds and how the ions are arranged tell us a lot about the solubility of the compound, solubility and other properties like melting or boiling points. It even can be related back to things like how hard a particular ionic solid is.

So the ionic bonds here in sodium chloride are the ones that hold together our sodium ions and our chloride ions. So our sodium plus and our chloride minus. The strength of an ionic bond is related to the electrostatic force—the electrostatic force between them.

I'm going to abbreviate the electrostatic force as F subscript e. So this is the force between two charged species, and it's equal to some constant K times the two charges that are interacting divided by the distance between the two charges squared. So here, q1 and Q2 are the charges, and in the case of sodium chloride, for example, q1 and Q2 would be—q1 might be 1 plus from our sodium ion, and Q2 might be 1 minus from our chloride ion.

We could also just switch those two; we could say chloride is q1 and sodium is Q2, and that wouldn't change what we get from this equation. And then R2 here is the distance between the ions, and we usually approximate it as saying it's a sum of the ionic radii for the two ions we're looking at.

So we can use Coulomb's law here to explain some properties that are related to the strengths of ionic bonds. The example we're going to go through today is going to be that of melting point.

So we're going to look at some melting point trends and try to relate them to the different variables in Coulomb's law. The first thing we'll look at—the first two compounds we'll compare are sodium fluoride and magnesium oxide. Sodium fluoride has a melting point of 993 °C, and magnesium oxide has a melting point of 2852 °C.

The other information we know about these two compounds—if you look up the ionic radii, it turns out that sodium fluoride, the distance between the ions, is about the same as magnesium oxide. They're not exactly the same, but they're pretty close. So if we were to say that R is approximately the same for these two, then we can explain the difference in melting points using the charges.

Since melting point is a measure of basically how much energy you need to add to these compounds to break apart your ions, we would expect the melting point to increase as Fe increases; as the force between the ions increases, we would expect to have to add more energy to break those ions apart.

We can see that in our first example, magnesium oxide. If we look at the charges on the ions, magnesium is 2 plus and oxide is 2 minus. In sodium fluoride, sodium is 1 plus and fluoride is 1 minus. So we would expect, assuming that R is about the same, that q1 * q2 is four times bigger in magnesium oxide versus sodium fluoride.

So q1 and q2—the product of q1 and q2—is higher for magnesium oxide, and that's why we would expect the melting point to be higher. We can also look at sodium chloride versus sodium fluoride, and in this case, let's look at—well, I don't know, maybe this is kind of artificial—the boiling point.

The melting point—sorry, the melting point of sodium chloride is 801 °C, and the melting point of sodium fluoride is, like we said earlier, 993 °C. This time, the charges are the same on our ions; our q1 and q2 are 1 plus for the sodium in both compounds and 1 minus for the chloride and the fluoride.

So q1 * q2 didn't change for these two compounds, but since we changed the anion from fluoride to chloride, we increased R here. Increasing R in the denominator makes the electrostatic force go down. Another way we could put it is that since R decreases as we go from sodium chloride to sodium fluoride, the melting point goes up.

So in each of these pairs, the compound that has the higher melting point is the one that also has the higher electrostatic forces, and that's either because the charges are higher—q1 and q2 are higher—or because the distance between the ions went down.

So these are some examples for how we can relate the properties of ionic compounds to the electrostatic force using Coulomb's law between the cation and the anion.